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Numerical algorithm based on Haar-Sinc collocation method for solving the hyperbolic PDEs.

Pirkhedri A, Javadi HH, Navidi HR - ScientificWorldJournal (2014)

Bottom Line: The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices.This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients.To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran.

ABSTRACT
The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed.

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Plot of the absolute errors for different values of k with t = 0.5 and n = 3 for Example 1.
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Related In: Results  -  Collection


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fig1: Plot of the absolute errors for different values of k with t = 0.5 and n = 3 for Example 1.

Mentions: Also, Figure 1 displays the convergence rate of our method with k = 4, 8, 16, 32 for t = 0.5. It is seen from the Figure 1 that for each fixed point (x, t) the absolute errors get smaller and smaller as k increases. Furthermore, we can see that the presented method provides accurate results even by using n = 3.


Numerical algorithm based on Haar-Sinc collocation method for solving the hyperbolic PDEs.

Pirkhedri A, Javadi HH, Navidi HR - ScientificWorldJournal (2014)

Plot of the absolute errors for different values of k with t = 0.5 and n = 3 for Example 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4248428&req=5

fig1: Plot of the absolute errors for different values of k with t = 0.5 and n = 3 for Example 1.
Mentions: Also, Figure 1 displays the convergence rate of our method with k = 4, 8, 16, 32 for t = 0.5. It is seen from the Figure 1 that for each fixed point (x, t) the absolute errors get smaller and smaller as k increases. Furthermore, we can see that the presented method provides accurate results even by using n = 3.

Bottom Line: The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices.This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients.To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran.

ABSTRACT
The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed.

Show MeSH